Polytope of Type {24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*192a
Also Known As : {24,4|2}. if this polytope has another name.
Group : SmallGroup(192,291)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 24, 48, 4
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {24,4,2} of size 384
   {24,4,4} of size 768
   {24,4,6} of size 1152
   {24,4,3} of size 1152
   {24,4,6} of size 1728
   {24,4,10} of size 1920
Vertex Figure Of :
   {2,24,4} of size 384
   {4,24,4} of size 768
   {4,24,4} of size 768
   {4,24,4} of size 768
   {4,24,4} of size 768
   {6,24,4} of size 1152
   {6,24,4} of size 1152
   {6,24,4} of size 1152
   {3,24,4} of size 1152
   {10,24,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*96a, {24,2}*96
   3-fold quotients : {8,4}*64a
   4-fold quotients : {12,2}*48, {6,4}*48a
   6-fold quotients : {4,4}*32, {8,2}*32
   8-fold quotients : {6,2}*24
   12-fold quotients : {2,4}*16, {4,2}*16
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,4}*384a, {24,8}*384a, {24,8}*384b, {48,4}*384a, {48,4}*384b
   3-fold covers : {72,4}*576a, {24,12}*576c, {24,12}*576d
   4-fold covers : {24,8}*768a, {24,4}*768a, {24,8}*768d, {48,4}*768a, {48,4}*768b, {24,16}*768a, {24,16}*768b, {48,8}*768c, {48,8}*768d, {24,16}*768d, {48,8}*768e, {48,8}*768f, {24,16}*768f, {96,4}*768a, {96,4}*768b, {24,4}*768i
   5-fold covers : {24,20}*960a, {120,4}*960a
   6-fold covers : {72,4}*1152a, {24,12}*1152a, {24,12}*1152b, {72,8}*1152b, {72,8}*1152c, {24,24}*1152b, {24,24}*1152c, {24,24}*1152e, {24,24}*1152g, {144,4}*1152a, {48,12}*1152a, {48,12}*1152b, {144,4}*1152b, {48,12}*1152d, {48,12}*1152e
   7-fold covers : {24,28}*1344a, {168,4}*1344a
   9-fold covers : {216,4}*1728a, {72,12}*1728a, {72,12}*1728b, {24,36}*1728c, {24,12}*1728c, {24,12}*1728d, {24,12}*1728o, {24,4}*1728e, {24,4}*1728f, {24,12}*1728u
   10-fold covers : {120,4}*1920a, {24,20}*1920a, {120,8}*1920b, {120,8}*1920c, {24,40}*1920a, {24,40}*1920b, {240,4}*1920a, {48,20}*1920a, {240,4}*1920b, {48,20}*1920b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)
(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)
(36,47)(50,51)(53,54)(56,57)(59,60)(61,64)(62,66)(63,65)(67,70)(68,72)(69,71)
(73,85)(74,87)(75,86)(76,88)(77,90)(78,89)(79,91)(80,93)(81,92)(82,94)(83,96)
(84,95);;
s1 := ( 1,26)( 2,25)( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)
(11,34)(12,36)(13,41)(14,40)(15,42)(16,38)(17,37)(18,39)(19,47)(20,46)(21,48)
(22,44)(23,43)(24,45)(49,74)(50,73)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)
(57,81)(58,83)(59,82)(60,84)(61,89)(62,88)(63,90)(64,86)(65,85)(66,87)(67,95)
(68,94)(69,96)(70,92)(71,91)(72,93);;
s2 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)
(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)
(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)
(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)
(44,86)(45,87)(46,88)(47,89)(48,90);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)
(21,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)
(35,48)(36,47)(50,51)(53,54)(56,57)(59,60)(61,64)(62,66)(63,65)(67,70)(68,72)
(69,71)(73,85)(74,87)(75,86)(76,88)(77,90)(78,89)(79,91)(80,93)(81,92)(82,94)
(83,96)(84,95);
s1 := Sym(96)!( 1,26)( 2,25)( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)
(10,35)(11,34)(12,36)(13,41)(14,40)(15,42)(16,38)(17,37)(18,39)(19,47)(20,46)
(21,48)(22,44)(23,43)(24,45)(49,74)(50,73)(51,75)(52,77)(53,76)(54,78)(55,80)
(56,79)(57,81)(58,83)(59,82)(60,84)(61,89)(62,88)(63,90)(64,86)(65,85)(66,87)
(67,95)(68,94)(69,96)(70,92)(71,91)(72,93);
s2 := Sym(96)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)
(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)
(21,69)(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)
(32,74)(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)
(43,85)(44,86)(45,87)(46,88)(47,89)(48,90);
poly := sub<Sym(96)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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